基于粒子群算法的发动机共同工作方程组求解

Application of Particle Swarm Optimization in Solution to Nonlinear Equations of Aeroengine Component Model

寻求一组能使共同工作方程组收敛的试给参数是确定航空发动机设计点的难点,为克服传统求解方法中,因试给参数与经验密切相关造成方程组收敛率和收敛速度较低的问题,在基本粒子群算法的基础上,综合能加速收敛的收敛因子和具有明确社会性定义的被动聚集压力因子,提出一种新的用于求解发动机共同工作方程组的粒子群算法,并称之为CPCPSO。前者能增加粒子的振幅,减少无效迭代,从而加速算法运行速度;后者能在不增加种群规模的前提下增加种群多样性。经仿真验证,针对两个不同的初始试给参数,CPCPSO算法均能使共同工作方程组收敛,且达到收敛时的总迭代次数更少。结果表明,CPCPSO算法克服了N+1残量法对共同工作方程组初值的依赖性,收敛速度快,试给参数确定更加有效。

The key in confirmation of design point is to seek a group of trial values which are suitable for the component model. The convergence rate and speed of traditional algorithm to nonlinear equations of aeroengine component model depend on the initial values. In the paper, particle swarm optimization （PSO） algorithm was used to overcome these shortages. To avoid local minimum, the CPCPSO was proposed, in which constriction factor and passive congregation factor were integrated. The former was used to accelerate the method by increase in particle amplitude. The later was used to increase the population variety without increase in population scale. The simulation results show that CPCPSO can converg faster, given two different initial values. It means that the CPCPSO algorithm overcomes the dependence on initial values and achieves faster convergence speed.